From f1bbec8a37aa8d7c0186d5851c90d015e55ed6a1 Mon Sep 17 00:00:00 2001
From: Pierre Santagostini <pierre.santagostini@agrocampus-ouest.fr>
Date: Thu, 6 Feb 2025 15:45:18 +0100
Subject: [PATCH] `kummerM()`: `eps` argument added. Help page: further
elements in the Details section.
---
R/estparnormratio.R | 41 ++++++++++++++++++++++++++++-------------
1 file changed, 28 insertions(+), 13 deletions(-)
diff --git a/R/estparnormratio.R b/R/estparnormratio.R
index 230eb59..f32ea83 100644
--- a/R/estparnormratio.R
+++ b/R/estparnormratio.R
@@ -12,19 +12,34 @@ estparnormratio <- function(z, eps = 1e-06) {
#' @usage estparnormratio(z, eps = 1e-6)
#' @param z numeric matrix or data frame.
#' @param eps numeric. Precision for the estimation of the parameters.
- #' @return A list of 5 elements:
- #' \itemize{
- #' \item \code{x}: the mean \eqn{\hat{\mu}_x} and standard deviation \eqn{\hat{\sigma}_x} of the first distribution.
- #' \item \code{y}: the mean \eqn{\hat{\mu}_y} and standard deviation \eqn{\hat{\sigma}_y} of the second distribution.
- #' \item \code{beta}, \code{rho}, \code{delta}: the parameters of the \eqn{Z} distribution:
- #' \eqn{\displaystyle{\hat{\delta}_y = \frac{\hat{\sigma}_y}{\hat{\mu}_y}}},
- #' \eqn{\displaystyle{\hat{\beta} = \frac{\hat{\mu}_x}{\hat{\mu}_y}}},
- #' \eqn{\displaystyle{\hat{\rho} = \frac{\hat{\sigma}_y}{\hat{\sigma}_x}}}.
- #' }
+ #' @return A list of 3 elements \code{beta}, \code{rho}, \code{delta}:
+ #' the parameters of the \eqn{Z} distribution:
+ #' \eqn{\hat{\beta}}, \eqn{\hat{\rho}}, \eqn{\hat{\delta}_y},
#' with two attributes \code{attr(, "epsilon")} (precision of the result) and \code{attr(, "k")} (number of iterations).
#'
- #' @details The parameters \eqn{\beta}, \eqn{\rho}, \eqn{\delta_y} are estimated with the EM algorithm
- #' as presented in El Ghaziri et al. The computation uses the \code{\link{kummerM}} function.
+ #' @details Let a random variable: \eqn{\displaystyle{Z = \frac{X}{Y}}},
+ #'
+ #' \eqn{X} and \eqn{Y} being normally distributed:
+ #' \eqn{X \sim N(\mu_x, \sigma_x)} and \eqn{Y \sim N(\mu_y, \sigma_y)}.
+ #'
+ #' The density probability of \eqn{Z} is:
+ #' \deqn{\displaystyle{
+ #' f_Z(z; \beta, \rho, \delta_y) = \frac{\rho}{\pi (1 + \rho^2 z^2)} \ \exp{\left(-\frac{\rho^2 \beta^2 + 1}{2\delta_y^2}\right)} \ {}_1 F_1\left( 1, \frac{1}{2}; \frac{1}{2 \delta_y} \frac{(1 + \beta \rho^2 z)^2}{1 + \rho^2 z^2} \right)
+ #' }}
+ #'
+ #' where: \eqn{\displaystyle{\hat{\beta} = \frac{\hat{\mu}_x}{\hat{\mu}_y}}},
+ #' \eqn{\displaystyle{\hat{\rho} = \frac{\hat{\sigma}_y}{\hat{\sigma}_x}}},
+ #' \eqn{\displaystyle{\hat{\delta}_y = \frac{\hat{\sigma}_y}{\hat{\mu}_y}}}.
+ #'
+ #' and \eqn{_1 F_1\left(a, b; x\right)} is the confluent \eqn{D}-hypergeometric function:
+ #' \deqn{\displaystyle{
+ #' _1 F_1\left(a, b; x\right) = \sum_{n = 0}^{+\infty}{ \frac{ (a)_n }{ (b)_n } \frac{x^n}{n!} }
+ #' }}
+ #'
+ #' The parameters \eqn{\beta}, \eqn{rho}, \eqn{delta_y} of the \eqn{Z} distribution
+ #' are estimated with the EM algorithm, as presented in El Ghaziri et al.
+ #' The computation uses the \code{\link{kummerM}} function.
+ #'
#' This uses an iterative algorithm.
#'
#' The precision for the estimation of the parameters is given by the \code{eps} parameter.
@@ -67,11 +82,11 @@ estparnormratio <- function(z, eps = 1e-06) {
#' @export
kummA <- function(x) {
- Re(kummerM(2, 1.5, x))/Re(kummerM(1, 0.5, x))
+ Re(kummerM(2, 1.5, x))/Re(kummerM(1, 0.5, x, eps = eps))
}
kummB <- function(x) {
- Re(kummerM(2, 0.5, x))/Re(kummerM(1, 0.5, x))
+ Re(kummerM(2, 0.5, x))/Re(kummerM(1, 0.5, x, eps = eps))
}
# Number of observations
--
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